a body weights 450N on the surface of the earth.How much will it weigh on the surface of a planet whose mass is 1/9th mass of earth and radius is half of radius of earth
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Answers
Answer:-
Let the mass of the earth be "M" and it's radius be R.
Given:
Weight of the object on the earth = 450 N
We know that,
Gravitational force (F) = GMm/r²
Where, m is the Mass of the object and G is the gravitational constant.
→ F between Object and earth = GMm/r²
→ GMm/r² = 450 N. -- equation (1)
And,
Mass of the planet = 1/9 * mass of earth
→ Mass of the planet = 1/9 * M = M/9
Radius of the planet = 1/2 * radius of earth
→ Radius of the planet = 1/2 * (r) = r/2
Hence,
→ F between Object and planet = (G * M/9 * m) / (r/2)²
→ F between Object and planet = [ (GMm) / 9 ] / (r² / 4)
→ F between Object and planet = (GMm) / 9 * (4 / r²)
→ F between Object and planet = (GMm) / r² * 4/9
Putting the values from equation (1) we get,
→ F between Object and planet = 450 * 4 / 9
→ F between Object and planet = 200 N
Hence, the Object weighs 200 N on the planet.